![OpenAI Astra: Ten Maths Breakthroughs](https://cdn.slatesource.com/c/f/8/cf89fdcc-bd8b-46d6-bd1c-37e19db415ed.webp) # OpenAI Astra: Ten Maths Breakthroughs - [Made in Slatesource](https://slatesource.com/@steph/openai-astra-ten-maths-breakthroughs) - By [Steph](https://slatesource.com/@steph) - Created on Aug 4, 2026 Open problems solved 10 Fields of mathematics covered 8 Compute cost to solve all ten approx. 2,000 USD Longest time any problem had been open over 25 years Length of accompanying manuscript 249 pages Lean 4 machine-checkable proofs published 10 of 10 ## What Is AstraAstra OpenAI'sOpenAI's nextnext majormajor modelmodel familyfamily has a namename: AstraAstra. But it did not arrivearrive with a presspress conferenceconference or a benchmarkbenchmark leaderboardleaderboard. On 1 AugustAugust 20262026, researcherresearcher NoamNoam BrownBrown pushedpushed tenten machine-checkablemachine-checkable mathematicalmathematical proofsproofs to GitHubGitHub and wrotewrote a briefbrief postpost callingcalling AstraAstra "our nextnext majormajor modelmodel." The problemsproblems it had solvedsolved had seenseen no meaningfulmeaningful progressprogress for at leastleast a decadedecade. MostMost had been openopen for muchmuch longerlonger. AstraAstra is describeddescribed as a "long-horizonlong-horizon" systemsystem, designeddesigned to workwork on extendedextended taskstasks autonomouslyautonomously ratherrather than answeranswer questionsquestions in a singlesingle exchangeexchange. The publicpublic releaserelease datedate, modelmodel sizesize, contextcontext windowwindow, and APIAPI priceprice are all unknownunknown. What is knownknown is that an internalinternal versionversion of AstraAstra, stillstill unreleasedunreleased, crackedcracked tenten problemsproblems acrossacross eighteight distinctdistinct fieldsfields of mathematicsmathematics and theoreticaltheoretical computercomputer sciencescience. journey·10 Steps # How Astra Proved Ten Unsolved Problems Field / Step The Announcement (1 August 2026) Launch "OpenAI researcher Noam Brown posts a brief note naming Astra as the company's next major model. No product details, no benchmark scores. Just ten proofs on GitHub and a 249-page manuscript." The non-sofic groups result (Gromov, 1999) is considered the single most significant of the ten. Non-sofic groups are mathematical objects that cannot be approximated by finite permutation groups. Their existence had been conjectured but never proven. Astra produced a constructive proof. The total compute cost for all ten results was approximately 2,000 USD at Sol API rates, the same model family used in OpenAI's consumer products. Elon Musk responded to the announcement on X with the words: "Welcome to the Singularity." ## What This ChangesChanges The significancesignificance is not just the resultsresults themselvesthemselves. EveryEvery priorprior AI mathsmaths milestonemilestone (AlphaProofAlphaProof, GPT-5GPT-5 solvingsolving competitioncompetition problemsproblems) involvedinvolved closed-formclosed-form answersanswers to well-definedwell-defined problemsproblems. Astra'sAstra's tenten resultsresults are open-endedopen-ended contributionscontributions: newnew constructionsconstructions, newnew boundsbounds, and newnew disproofsdisproofs that professionalprofessional mathematiciansmathematicians had not producedproduced. The LeanLean 4 certificatescertificates changechange the epistemologyepistemology of mathematicalmathematical discoverydiscovery. InsteadInstead of waitingwaiting monthsmonths for peerpeer reviewreview, anyoneanyone can runrun the certificatecertificate and confirmconfirm the proofproof is validvalid in minutesminutes. If this scalesscales, the pacepace of mathematicalmathematical progressprogress couldcould accelerateaccelerate in waysways that are difficultdifficult to projectproject. The costcost of a decadedecade of unsolvedunsolved problemsproblems just droppeddropped to roughlyroughly twotwo thousandthousand dollarsdollars. > These are big news. More significant than the unit distance counterexample announced in May. Astra has not launched publicly. OpenAI has not confirmed a release date, model size, context window, or price. The internal version that produced these results may differ substantially from the product that eventually ships. Polymarket puts an August 31 public release at approximately 24 percent probability. [BleepingComputer: OpenAI teases Astra after solving 10 long-standing maths problems](https://www.bleepingcomputer.com/news/artificial-intelligence/openai-teases-astra-its-next-major-ai-model-after-it-solves-10-long-standing-math-problems/?utm_source=slatesource) [Forbes: OpenAI's Astra solved decades-old maths problems for 2,000 dollars](https://www.forbes.com/sites/jonmarkman/2026/08/03/openais-astra-solved-10-decades-old-math-problems-for-just-2000/?utm_source=slatesource)